Descriptive Statistics Quiz

PDF page 139: box plot a graph that gives a quick picture of the middle 50 percent of the data first quartile the value that is the median of the lower half of the ordered data set frequency the number of times a value of the data occurs frequency polygon a data display that looks like a line graph but uses intervals to display ranges of large amounts of data frequency table a data representation in which grouped data are displayed along with the corresponding frequencies histogram a graphical representation in x-y form of the distribution of data in a data set; x represents the data and y represents the frequency, or relative frequency; the graph consists of contiguous rectangles interquartile range or IQR, is the range of the middle 50 percent of the data values; the IQR is found by subtracting the first quartile from the third quartile interval also called a class interval; an interval represents a range of data and is used when displaying large data sets mean a number that measures the central tendency of the data; a common name for mean is average. ̄ The term mean is a shortened form of arithmetic mean. By definition, the mean for a sample (denoted by x ) is Sum of all values in the sample ̄ x =

PDF page 140: (Q2 or median) is the 50 percentile, and the third quartile (Q3) is the 75 percentile. The interquartile range, or IQR, is the range of the middle 50 percent of the data values. The IQR is found by subtracting Q1 from Q3 and can help determine outliers by using the following two expressions.

PDF page 140: The mean and the median can be calculated to help you find the center of a data set. The mean is the best estimate for the actual data set, but the median is the best measurement when a data set contains several outliers or extreme values. The mode will tell you the most frequently occurring datum (or data) in your data set. The mean, median, and mode are extremely helpful when you need to analyze your data, but if your data set consists of ranges that lack specific values, the mean may seem impossible to calculate. However, the mean can be approximated if you add the lower boundary with the upper boundary and divide by two to find the midpoint of each interval. Multiply each midpoint by the number of values found in the corresponding range. Divide the sum of these values by the total number of data values in the set.

PDF page 140: The mean and the median can be calculated to help you find the center of a data set. The mean is the best estimate for the actual data set, but the median is the best measurement when a data set contains several outliers or extreme values. The mode will tell you the most frequently occurring datum (or data) in your data set. The mean, median, and mode are extremely helpful when you need to analyze your data, but if your data set consists of ranges that lack specific values, the mean may seem impossible to calculate. However, the mean can be approximated if you add the lower boundary with the upper boundary and divide by two to find the midpoint of each interval. Multiply each midpoint by the number of values found in the corresponding range. Divide the sum of these values by the total number of data values in the set.

PDF page 139: skewed used to describe data that is not symmetrical; when the right side of a graph looks chopped off compared to the left side, we say it is skewed to the left. When the left side of the graph looks chopped off compared to the right side, we say the data are skewed to the right. Alternatively, when the lower values of the data are more spread out, we say the data are skewed to the left. When the greater values are more spread out, the data are skewed to the right. standard deviation a number that is equal to the square root of the variance and measures how far data values are from their mean; notation: s for sample standard deviation and σ for population standard deviation

PDF page 139: median of the data is the second quartile and the 50 percentile

PDF page 140: observations in the set. Quartiles divide data into quarters. The first quartile (Q1) is the 25 percentile, the second quartile

PDF page 139: skewed used to describe data that is not symmetrical; when the right side of a graph looks chopped off compared to the left side, we say it is skewed to the left. When the left side of the graph looks chopped off compared to the right side, we say the data are skewed to the right. Alternatively, when the lower values of the data are more spread out, we say the data are skewed to the left. When the greater values are more spread out, the data are skewed to the right. standard deviation a number that is equal to the square root of the variance and measures how far data values are from their mean; notation: s for sample standard deviation and σ for population standard deviation

PDF page 140: A stem-and-leaf plot is a way to plot data and look at the distribution. In a stem-and-leaf plot, all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends, that is, finding a general pattern in data sets, including temperature, sales, employment, company profit, or cost, over a period of time. A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories. One axis of the chart shows the specific categories being compared, and the other axis represents a discrete value. Bar graphs are especially useful when categorical data are being used.

PDF page 140: A stem-and-leaf plot is a way to plot data and look at the distribution. In a stem-and-leaf plot, all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends, that is, finding a general pattern in data sets, including temperature, sales, employment, company profit, or cost, over a period of time. A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories. One axis of the chart shows the specific categories being compared, and the other axis represents a discrete value. Bar graphs are especially useful when categorical data are being used.

PDF page 140: A stem-and-leaf plot is a way to plot data and look at the distribution. In a stem-and-leaf plot, all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends, that is, finding a general pattern in data sets, including temperature, sales, employment, company profit, or cost, over a period of time. A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories. One axis of the chart shows the specific categories being compared, and the other axis represents a discrete value. Bar graphs are especially useful when categorical data are being used.

PDF page 139: box plot a graph that gives a quick picture of the middle 50 percent of the data first quartile the value that is the median of the lower half of the ordered data set frequency the number of times a value of the data occurs frequency polygon a data display that looks like a line graph but uses intervals to display ranges of large amounts of data frequency table a data representation in which grouped data are displayed along with the corresponding frequencies histogram a graphical representation in x-y form of the distribution of data in a data set; x represents the data and y represents the frequency, or relative frequency; the graph consists of contiguous rectangles interquartile range or IQR, is the range of the middle 50 percent of the data values; the IQR is found by subtracting the first quartile from the third quartile interval also called a class interval; an interval represents a range of data and is used when displaying large data sets mean a number that measures the central tendency of the data; a common name for mean is average. ̄ The term mean is a shortened form of arithmetic mean. By definition, the mean for a sample (denoted by x ) is Sum of all values in the sample ̄ x =

PDF page 140: Box plots are a type of graph that can help visually organize data. Before a box plot can be graphed, the following data points must be calculated: the minimum value, the first quartile, the median, the third quartile, and the maximum value. Once the box plot is graphed, you can display and compare distributions of data.